For a four-dimensional array a[i][j][k][l] in C, which equivalent pointer expression correctly refers to that element using pointer arithmetic and dereferencing?

Introduction / Context:
In C, multi-dimensional arrays are arrays of arrays laid out contiguously in row-major order. Subscript notation a[i][j][k][l] can be expressed using pointer arithmetic and dereferencing. This question checks your understanding of how nested dereferences correspond to each subscript level.

Given Data / Assumptions:

• a is declared as a true 4D array, not as a flattened pointer.
• Each subscript selects the next inner array level.
• Pointer arithmetic is scaled by the size of the pointed-to type at each level.

Concept / Approach:
For an array T a[A][B][C][D], the expression a+i advances i elements of type T[B][C][D]. Dereferencing once with * yields a[i], which is of type T[B][C][D]. Repeating this logic, each subsequent + index and * dereference steps into the next dimension until reaching the scalar element T at [i][j][k][l].

Step-by-Step Solution:
Start: a+i → pointer to a[i] (type: array of [B][C][D]).Dereference: (a+i) → a[i].Add j: (a+i)+j → &a[i][j] (pointer to array [C][D]).Dereference: ((a+i)+j) → a[i][j].Add k: ((a+i)+j)+k → &a[i][j][k] (pointer to array [D]).Dereference: (((a+i)+j)+k) → a[i][j][k].Add l: (((a+i)+j)+k)+l → &a[i][j][k][l].Final dereference: ((((a+i)+j)+k)+l) → a[i][j][k][l].

Verification / Alternative check:
For a 2D case a[i][j], the equivalent (a[i] + j) generalizes to higher dimensions by nesting the pattern consistently, confirming the chosen expression.

Why Other Options Are Wrong:

• Parentheses-only sums like (((a+i)+j)+k+l) never dereference; they also add integers to incompatible pointer types.
• ((((a+i)+j)+k)+l) similarly omits dereferencing at each dimension.

Common Pitfalls:
Forgetting that each dimension requires a dereference before adding the next index; otherwise, types do not line up and the expression becomes ill-formed.

Final Answer:
(((*(a+i)+j)+k)+l).